Keep Operator Properties popup expanded
This setting is saved with the startup file preferences.

On a blank startup file just use some operator (like say Add > Plane) and expand the operator options panel once (you can delete the object or undo afterwards if you like).

After expanding the panel go to File > Defaults > Save Startup File and next time you call any operator with options it will be expanded.



Since this is saved in the startup file, it should be available in all new Blender sessions as well.